📚 Year 7 WJEC Maths: Core Topics Overview | Year 7 WJEC 数学：核心知识点梳理
Welcome to your Year 7 WJEC Maths revision guide. This article brings together all the core topics you will meet in Year 7, from number operations and fractions to geometry and data handling. Each section is explained clearly with paired English and Chinese explanations, helping you build confidence and secure the foundations you need for future study.
欢迎阅读 Year 7 WJEC 数学复习指南。本文汇集了你在七年级会接触到的全部核心主题，从数的运算、分数到几何和数据处理。每个部分都用配对的中英文解释进行清晰说明，帮助你建立信心并打下未来学习所需的扎实基础。
1. Number and Place Value | 数字与位值
Understanding place value means knowing that the position of a digit gives its value. For whole numbers, we work with units, tens, hundreds, thousands, ten thousands and so on.
理解位值就是知道数字的位置决定它的值。对于整数，我们使用的是个位、十位、百位、千位、万位等等。
For example, in 6,305 the digit 6 is in the thousands place and represents 6,000, while 3 is in the hundreds place (300), 0 tens and 5 units.
例如，在 6,305 中，数字 6 位于千位，表示 6,000；3 在百位（300）；0 个十；5 个一。
You will also practise rounding numbers to the nearest 10, 100 or 1,000 to make estimates and check answers. For instance, 487 rounded to the nearest 100 is 500.
你还需要练习将数字四舍五入到最接近的十位、百位或千位，以便进行估算和验算。例如，487 四舍五入到百位是 500。
2. Addition and Subtraction of Whole Numbers | 整数的加法与减法
We use column addition and column subtraction for larger numbers. When adding, we may need to carry into the next column if a column total is 10 or more. When subtracting, we sometimes borrow from a higher place value.
对于较大的数，我们使用竖式加法和竖式减法。加法时，如果某一列的总和达到或超过 10，就需要向前一列进位。减法时，有时需要从更高的位值借位。
Mental strategies, such as partitioning numbers into hundreds, tens and ones before adding, are equally important. For example, 245 + 132 can be thought of as (200+100) + (40+30) + (5+2) = 300 + 70 + 7 = 377.
心算策略同样重要，例如在加法前将数字拆分成百位、十位和个位。比如 245 + 132 可以拆成 (200+100) + (40+30) + (5+2) = 300 + 70 + 7 = 377。
3. Multiplication and Division | 乘法与除法
Multiplication is repeated addition, and division is sharing into equal groups. By the end of Year 7, you should be confident with times tables up to 12 × 12 and be able to use written methods for multiplying and dividing larger numbers.
乘法是重复的加法，除法是平均分组。在七年级结束时，你应该能够熟练掌握到 12 × 12 的乘法表，并能够使用书面方法进行较大数的乘法和除法。
For multiplication of a two‑digit number by another two‑digit number, we often use the grid method or long multiplication. For example, 43 × 26 can be calculated by splitting 43 into 40 and 3, and 26 into 20 and 6, then finding the four partial products.
对于两位数乘以两位数，我们常用网格法或长乘法。例如，43 × 26 可以将 43 拆成 40 和 3，将 26 拆成 20 和 6，然后求出四个部分积再相加。
Division can be handled by short division (bus stop method) or by chunking. The relationship between multiplication and division is also key: 84 ÷ 6 = 14 because 14 × 6 = 84.
除法可以用短除法（公交车站法）或分块法处理。乘法和除法的逆运算关系也很关键：84 ÷ 6 = 14，因为 14 × 6 = 84。
4. Introduction to Fractions | 分数入门
A fraction represents a part of a whole. The denominator (bottom number) tells us how many equal parts the whole is divided into, and the numerator (top number) tells us how many parts we have.
分数表示整体的一部分。分母（下方的数）告诉我们整体被分成了多少等份，分子（上方的数）告诉我们要取出多少份。
You will work with equivalent fractions, such as ½ = ²⁄₄ = ⁴⁄₈, and learn to simplify fractions by dividing numerator and denominator by their highest common factor (HCF). Compare fractions by converting them to the same denominator or by using decimal equivalents.
你将学习等值分数，例如 ½ = ²⁄₄ = ⁴⁄₈，并学会通过分子和分母除以它们的最大公因数来约分。比较分数时可以将它们化成同分母，或者利用它们对应的小数。
Adding and subtracting fractions with the same denominator is straightforward: ³⁄₈ + ²⁄₈ = ⁵⁄₈. When denominators differ, you first need to write the fractions with a common denominator.
同分母分数的加法和减法很简单：³⁄₈ + ²⁄₈ = ⁵⁄₈。当分母不同时，你需要先将这些分数化为有共同分母的形式。
5. Decimals and Their Operations | 小数及其运算
Decimals are another way of writing fractions with denominators of 10, 100, 1000, etc. The number 0.37 means 37 hundredths, and 0.3 means 3 tenths.
小数是分母为 10、100、1000 等的分数的另一种写法。0.37 表示百分之三十七，0.3 表示十分之三。
You will order decimals by comparing digits in the tenths, hundredths and thousandths places. For calculation, addition and subtraction of decimals involve keeping the decimal points lined up in columns.
你需要通过比较十分位、百分位和千分位的数字来排列小数。进行小数的加法和减法计算时，要使小数点对齐成列。
Multiplying a decimal by a whole number is similar to multiplying whole numbers, then placing the decimal point correctly. For example, 0.6 × 4 = 2.4. Dividing decimals, such as 3.5 ÷ 5 = 0.7, is practised with simple examples.
小数乘以整数的计算方法类似于整数乘法，然后再正确点上小数点。例如 0.6 × 4 = 2.4。小数的除法，如 3.5 ÷ 5 = 0.7，会通过简单例子进行练习。
6. Percentages | 百分比
Percent means ‘out of 100’. You will convert between fractions, decimals and percentages. For example, 25% = ¼ = 0.25, and 60% = ³⁄₅ = 0.6.
百分比的意思是“每一百个中的部分”。你将学习在分数、小数和百分数之间进行转换。例如，25% = ¼ = 0.25，60% = ³⁄₅ = 0.6。
Finding a percentage of an amount often starts with finding 10% by dividing by 10, and then using that to build other percentages. For instance, 30% of 80 is 3 × (10% of 80) = 3 × 8 = 24.
求一个量的百分比常常从除以 10 找到 10% 开始，然后利用它组合出其他百分比。例如，80 的 30% 是 3 × (80 的 10%) = 3 × 8 = 24。
7. Basic Algebra | 基础代数
Algebra uses letters to stand for unknown numbers. You will learn to write simple expressions, such as 3 more than n is n + 3, and 5 times a number is 5x.
代数用字母代表未知数。你将学会写出简单的表达式，例如比 n 大 3 的数表示为 n + 3，一个数的 5 倍表示为 5x。
Simplifying expressions by collecting like terms is an essential skill. For example, 2a + 5a = 7a, and 3x + 2y + x = 4x + 2y (because x and y are unlike).
通过合并同类项化简表达式是一项基本技能。例如，2a + 5a = 7a，3x + 2y + x = 4x + 2y（因为 x 和 y 是不同类项）。
You will also solve simple equations by keeping the balance. x + 5 = 12 means x = 7; and 3y = 18 gives y = 6.
你还会通过保持等式平衡来解简单方程。x + 5 = 12 的解是 x = 7；3y = 18 的解是 y = 6。
8. Geometry: Angles | 几何：角度
An angle measures the amount of turn between two lines meeting at a vertex. Angles are measured in degrees (°). Key angle facts include: angles on a straight line add up to 180°, angles around a point add up to 360°, and the angles inside a triangle sum to 180°.
角用来度量两条线在顶点处的张开程度。角以度数（°）为单位。重要的角度性质包括：平角（直线上的角）之和为 180°，绕一点一周的角度之和为 360°，以及三角形内角和为 180°。
You will classify angles as acute (less than 90°), right angle (exactly 90°), obtuse (between 90° and 180°) and reflex (greater than 180°).
你将学习把角分为锐角（小于 90°）、直角（等于 90°）、钝角（大于 90° 且小于 180°）和优角（大于 180°）。
Using a protractor to measure and draw angles is a key practical skill. You also learn to find missing angles using angle facts without a protractor.
使用量角器测量和绘制角度是一项关键的实践技能。你还会学习如何不用量角器，而是利用角度性质求出未知角。
9. Perimeter and Area | 周长与面积
The perimeter of a shape is the total distance around its edge. For a rectangle, perimeter = 2 × (length + width). You will also work with compound shapes made from rectangles.
形状的周长是它边界一圈的总长度。对于长方形，周长 = 2 ×（长 + 宽）。你还会处理由长方形组合而成的组合图形。
Area is the amount of space inside a 2D shape. The area of a rectangle is length × width. For example, a rectangle that is 5 cm by 3 cm has an area of 15 cm². You also learn that the area of a triangle is half the base × perpendicular height.
面积是二维图形内部空间的大小。长方形的面积 = 长 × 宽。例如，一个长 5 cm、宽 3 cm 的长方形面积是 15 cm²。你还会学到三角形的面积 = 底 × 垂直高度 ÷ 2。
10. Data Handling and Statistics | 数据处理与统计
You will collect, organise and represent data using tally charts, frequency tables, bar charts, pictograms and line graphs. The main purpose is to make data easier to understand and compare.
你将使用计数表、频数表、条形图、象形图和折线图来收集、整理和呈现数据。主要目的是让数据更容易理解和比较。
The mean (average) is found by adding all values and dividing by the number of values. The mode is the value that appears most often, and the range is the difference between the largest and smallest values.
平均数（均值）是将所有数值相加后除以数值的个数得到的。众数是出现次数最多的数值，极差是最大值与最小值之差。
You also begin to read and interpret data from real-life graphs, such as temperature line graphs or distance-time graphs.
你也会开始阅读和解读实际生活中的图表，如气温变化折线图或距离-时间图。
11. Probability Basics | 概率基础
Probability describes how likely an event is to happen, using words such as impossible, unlikely, even chance, likely and certain. On a probability scale from 0 to 1, 0 means impossible and 1 means certain.
概率描述一个事件发生的可能性大小，使用的词语包括：不可能、不太可能、均等机会、很可能和一定。在从 0 到 1 的概率标尺上，0 表示不可能，1 表示一定发生。
For a fair six-sided dice, the probability of rolling a 3 is ⅙. You work out probability as: number of favourable outcomes divided by total number of possible outcomes.
对于一个均匀的六面骰子，掷出 3 的概率是 ⅙。计算概率的方法是：符合要求的结果数 除以 所有可能的结果数。
You will also learn that the probabilities of all possible outcomes add up to 1.
你还会学到，所有可能结果的概率之和为 1。
12. Measure and Units | 度量与单位
In Year 7 you use standard metric units: length (mm, cm, m, km), mass (g, kg) and capacity/volume (ml, l). You will convert between units, for example 1 m = 100 cm, 1 kg = 1,000 g and 1 l = 1,000 ml.
在七年级，你需要使用标准公制单位：长度（毫米 mm、厘米 cm、米 m、千米 km），质量（克 g、千克 kg）和容量/体积（毫升 ml、升 l）。你要在单位间进行换算，例如 1 m = 100 cm，1 kg = 1,000 g，1 l = 1,000 ml。
Reading scales on measuring instruments such as rulers, weighing scales and measuring jugs is practised. You also solve problems involving time, including the 12‑ and 24-hour clock, and solve time interval problems using a number line or addition/subtraction.
你需要练习读取直尺、台秤和量杯等测量工具上的刻度。你还要解决关于时间的问题，包括 12 小时制和 24 小时制，并使用数线或加减法计算时间间隔。
Money calculations with pounds (£) and pence (p) continue to be revised, with the focus on giving change and solving real‑life problems.
英镑（£）和便士（p）的货币计算也会继续巩固，重点放在找零和解决实际问题上。
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